Both are designed by the NBCC- Some states require the NCE for licensure, some require the NCMHCE and believe it or not, some states require BOTH! UGh!.... The NCE is a multiple choice question type exam and covers many different areas, the NCMHCE concentrates on the DSM and 10 simulations.
In Illinois, the NCE is a required exam to obtain an LPC (LicensedProfessional Counselor). It is also required BEFORE you can take the NCMHCE; which is what they use as their test for the LCPC (Licensed Clinical Professional COunselor).